Wiskunde Multiple Choice Vraag

$\displaystyle\lim_{x\to4}\;\frac{2x^3-128}{\sqrt{x}-2}$ Het resultaat van deze limiet ligt in het interval	A. ] , 0 [
B. ] 0, 100 [
C. ] 100, 200 [
D. ] 200, 300 [
E. ] 300, [

IN CONS IN CONSTR IN CONSTRUC IN CONSTRUCTI IN CONSTRUCTION	A.
B.
C.
D.
E.

$\inline\displaystyle\lim_{x\to4}\;\frac{2x^3-128}{\sqrt{x}-2}=\lim_{x\to4}\;\frac{2(x^3-4^3)}{\sqrt{x}-2}=2\displaystyle\lim_{x\to4}\;\frac{(x-4)(x^2+4x+16)}{\sqrt x-2}\\=2\displaystyle\lim_{x\to4}\;\frac{(\sqrt x-2)(\sqrt x+2)(x^2+4x+16)}{\sqrt x-2}=2\displaystyle\lim_{x\to4}\;\left[(\sqrt x+2).(x^2+4x+16)\right]\\=2.(2+2).(16+16+16)=2.4.3.16=3.2^{7}=3.128=384$

^{gricha - vA155 - 30.3.2026}